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Thèse de Doctorat

Non-Coherent Detection of Continuous Phase Modulation for Low Earth Orbit Satellite IoT Communications Affected by Doppler Shift

Auteur : Jerbi Anouar

Defended on March 14, 2023.

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L’internet des objets (IoT) est un concept dans lequel de nombreux objets sont dotés de capacités de transmissions ou de communications via une connexion au réseau internet. Desservies essentiellement par des réseaux terrestres, des applications IoT peuvent également concerner les opérateurs satellites, par exemple dans les zones peu couvertes, ce qui ouvre ainsi des problématiques intéressantes au niveau de la couche physique de ces objets communicants. L’approche qui nous intéresse dans le but d’avoir une couverture globale du réseau IoT est le Direct-to-Satellite IoT [1]. Il s’agit d’une approche où aucune passerelle terrestre intermédiaire n’est requise, ce qui facilite et accélère le déploiement du réseau. Dans ce cadre, le satellite collecte directement les données des objets communicants et les traite. Il devrait également être capable de communiquer avec l’objet si une liaison descendante est envisagée. Cette approche pose certains problèmes en termes de couche physique. Le grand défi ici est de pouvoir créer une liaison de communication longue portée fiable ayant des ressources limitées à la fois dans le satellite et dans l’objet communicant tout en faisant face aux problèmes d’une liaison satellite. Cela peut être réalisé soit en révisant et en adaptant des technologies IoT existantes pour prendre en charge les communications directes avec un satellite, soit en fournissant de nouvelles couches MAC et physiques spécifiquement dédiées à cette application. Nous nous focalisons plutôt sur la deuxième approche. Lors du choix d’une forme d’onde pour n’importe quelle application de communication sans fil, trois éléments majeurs doivent être étudiés ; performances, complexité et bande passante. En général, la forme d’onde choisie est celle qui offre le meilleur compromis entre ces trois éléments. Pour les applications de communication par satellites en orbites basses, plusieurs dégradations majeures affectant les performances doivent être prises en compte. Les instabilités de phase, le décalage Doppler élevé, les interférences dans un scénario multi-utilisateurs, les amplificateurs non linéaires généralement utilisés des deux côtés de la transmission, au niveau des objets communicants et à bord du satellite, etc. En termes de complexité, il est important qu’elle soit la plus faible possible car dans l’application visée, les objets communicants utilisent de petites piles et le satellite n’est pas qu’un simple relais, mais au contraire, il effectue une partie du traitement et compte tenu des ressources limitées à bord, la complexité est une contrainte majeure. La bande passante dans l’application ciblée peut également être un problème. Que ce soit des bandes de fréquences sous licence ou non, la bande passante disponible est limitée. La modulation de phase continue (CPM) est une classe de modulation qui englobe plusieurs familles de formes d’onde de modulation de phase. Elle possède différents paramètres qui peuvent être ajustés pour répondre aux besoins de l’application. Les travaux de recherche portant sur la conception de formes d’onde CPM avec des systèmes de communication par satellites pour obtenir de bonnes performances du point de vue spectre et énergie ont montré des résultats prometteurs. Le problème de l’efficacité énergétique a été discuté dans [2] et [3]. Une étude sur la manière de choisir des schémas CPM spectralement efficaces a été présentée dans [4]. L’interférence du canal adjacent (ACI) a également été évaluée dans [5] et la possibilité d’utiliser des schémas de codage pour résoudre certains des problèmes mentionnés en utilisant la bande de fréquence Ka peut être trouvée dans [6]. Bien que les travaux cités ne s’appliquent peut-être pas spécifiquement à l’application Satellite IoT, ils fournissent cependant de bonnes bases fondatrices pour dériver des solutions adaptées à notre problème. Certains standards basés sur les communications par satellite utilisent déjà un format CPM. On peut citer le standard de diffusion vidéo numérique DVB-RCS2 [7] qui a été éditée par le consortium international DVB project. Plus récemment, un schéma GFSK a également été adopté par Semtech comme candidat pour la technique Long Range Frequency Hopping Spread Spectrum (LR-FHSS) [8]. Compte tenu de tous ces détails, nous avons choisi de nous concentrer sur la forme d’onde CPM dans ce travail pour exploiter son potentiel dans l’application considérée et nous avons particulièrement étudié sa réception du point de vue du satellite (lien montant).

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Communications numériques / Systèmes spatiaux de communication

Présentation de soutenance de thèse

Non-Coherent Detection of Continuous Phase Modulation for Low Earth Orbit Satellite IoT Communications Affected by Doppler Shift

Auteur : Jerbi Anouar

Defended on March 14, 2023.

Télécharger le document

L’internet des objets (IoT) est un concept dans lequel de nombreux objets sont dotés de capacités de transmissions ou de communications via une connexion au réseau internet. Desservies essentiellement par des réseaux terrestres, des applications IoT peuvent également concerner les opérateurs satellites, par exemple dans les zones peu couvertes, ce qui ouvre ainsi des problématiques intéressantes au niveau de la couche physique de ces objets communicants. L’approche qui nous intéresse dans le but d’avoir une couverture globale du réseau IoT est le Direct-to-Satellite IoT [1]. Il s’agit d’une approche où aucune passerelle terrestre intermédiaire n’est requise, ce qui facilite et accélère le déploiement du réseau. Dans ce cadre, le satellite collecte directement les données des objets communicants et les traite. Il devrait également être capable de communiquer avec l’objet si une liaison descendante est envisagée. Cette approche pose certains problèmes en termes de couche physique. Le grand défi ici est de pouvoir créer une liaison de communication longue portée fiable ayant des ressources limitées à la fois dans le satellite et dans l’objet communicant tout en faisant face aux problèmes d’une liaison satellite. Cela peut être réalisé soit en révisant et en adaptant des technologies IoT existantes pour prendre en charge les communications directes avec un satellite, soit en fournissant de nouvelles couches MAC et physiques spécifiquement dédiées à cette application. Nous nous focalisons plutôt sur la deuxième approche. Lors du choix d’une forme d’onde pour n’importe quelle application de communication sans fil, trois éléments majeurs doivent être étudiés ; performances, complexité et bande passante. En général, la forme d’onde choisie est celle qui offre le meilleur compromis entre ces trois éléments. Pour les applications de communication par satellites en orbites basses, plusieurs dégradations majeures affectant les performances doivent être prises en compte. Les instabilités de phase, le décalage Doppler élevé, les interférences dans un scénario multi-utilisateurs, les amplificateurs non linéaires généralement utilisés des deux côtés de la transmission, au niveau des objets communicants et à bord du satellite, etc. En termes de complexité, il est important qu’elle soit la plus faible possible car dans l’application visée, les objets communicants utilisent de petites piles et le satellite n’est pas qu’un simple relais, mais au contraire, il effectue une partie du traitement et compte tenu des ressources limitées à bord, la complexité est une contrainte majeure. La bande passante dans l’application ciblée peut également être un problème. Que ce soit des bandes de fréquences sous licence ou non, la bande passante disponible est limitée. La modulation de phase continue (CPM) est une classe de modulation qui englobe plusieurs familles de formes d’onde de modulation de phase. Elle possède différents paramètres qui peuvent être ajustés pour répondre aux besoins de l’application. Les travaux de recherche portant sur la conception de formes d’onde CPM avec des systèmes de communication par satellites pour obtenir de bonnes performances du point de vue spectre et énergie ont montré des résultats prometteurs. Le problème de l’efficacité énergétique a été discuté dans [2] et [3]. Une étude sur la manière de choisir des schémas CPM spectralement efficaces a été présentée dans [4]. L’interférence du canal adjacent (ACI) a également été évaluée dans [5] et la possibilité d’utiliser des schémas de codage pour résoudre certains des problèmes mentionnés en utilisant la bande de fréquence Ka peut être trouvée dans [6]. Bien que les travaux cités ne s’appliquent peut-être pas spécifiquement à l’application Satellite IoT, ils fournissent cependant de bonnes bases fondatrices pour dériver des solutions adaptées à notre problème. Certains standards basés sur les communications par satellite utilisent déjà un format CPM. On peut citer le standard de diffusion vidéo numérique DVB-RCS2 [7] qui a été éditée par le consortium international DVB project. Plus récemment, un schéma GFSK a également été adopté par Semtech comme candidat pour la technique Long Range Frequency Hopping Spread Spectrum (LR-FHSS) [8]. Compte tenu de tous ces détails, nous avons choisi de nous concentrer sur la forme d’onde CPM dans ce travail pour exploiter son potentiel dans l’application considérée et nous avons particulièrement étudié sa réception du point de vue du satellite (lien montant).

Lire la suite

Réseaux / Systèmes spatiaux de communication

Article de conférence

Improving AI Monitoring of Early Life Satellites Using Transfer Learning

Auteurs : Baron Audric, Lambert Pierre-Baptiste, Delande Pauline, Tourneret Jean-Yves, Lesouple Julien et Fabre Serge

In Proc. 17th International Conference on Space Operations (SpaceOps), Dubaï, United Arab Emirates, March 6-10, 2023.

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In the last decades, many space domain actors such as the Centre National d’Etudes Spatiales (CNES) have begun to use Artificial Intelligence to monitor spacecraft housekeeping telemetry. These novel techniques are able to identify atypical behaviours and potential satellite anomalies that cannot be detected by more standard monitoring approaches. However, AI methods have an important drawback: they need a significant amount of data to be able to “learn” the nominal behaviour of a spacecraft and then detect novelties in new telemetry, which is not suitable for a satellite in the beginning of life where in-flight telemetry is very scarce. One way to bypass the scarcity of data is Transfer Learning (TL). Depending on the use case, operators may have already-available telemetry either from on-the-ground Assembly, Integration, and Test (AIT) of the spacecraft, from full-digital or hybrid simulators, or from in-flight telemetry of one or multiple “twin-spacecraft” in case of a constellation with already-launched units. This already-available telemetry is often close, but not perfectly similar, to in-flight telemetry of the newly-launched spacecraft to be monitored. The idea of TL is therefore to use this large and existing database (the source database), coupled with the first in-flight telemetry from the new spacecraft (the target database), to be able to mathematically-design a relevant AI learning model. In 2022, CNES and TéSA laboratory have worked together and have identified two TL methods to detect anomalies in telemetry of early life satellites with few data, by working directly on the telemetry dataset (the learning domain) or on the model learned from the target database. The first TL method consists in mathematically modifying the decision boundary estimated by a One-Class Support Vector Machine (OC-SVM) algorithm applied to the source database to match the target database. The second method based on “Domain Transfer” consists in building an “extended” learning domain made up with the relevant data from both the source and target databases, which is used to build a learning model. These two algorithms have been evaluated with real Earth Observation satellite telemetry. The preliminary outcomes of this research show promising results. Further work will consist in implementing these methods operationally so that AI monitoring methods can be used from the very beginning-of-life of CNES satellites. The main conclusion of this work is that TL can be an interesting tool to monitor spacecraft housekeeping telemetry during the first 6 months after the launch of a satellite.

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Traitement du signal et des images / Systèmes spatiaux de communication

Article de journal

Band-limited impulse response estimation performance

Auteurs : Lubeigt Corentin, Ortega Espluga Lorenzo, Vilà-Valls Jordi et Chaumette Eric

Signal Processing, vol. 208, Art. no 108998, July, 2023.

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When a signal is strongly distorted by a reflecting surface, the surface can be seen as a filter whose impulse response is convoluted with the incident signal. Depending on the application, it can be useful to estimate this impulse response in order to either compensate or interpret it. When it comes to estimation, a performance lower bound should be computed in order to better understand the performance limits of the observation model at hand. Hence, a first contribution of this work is to provide an easy-to-use closed-form Cramér–Rao bound for the proposed signal model. The validation process of this lower bound raises the problem of the size, generally unknown, of the impulse response to be estimated. A second contribution of this study is then to provide adapted theoretical and practical tools to determine the size of a given impulse response along with its estimation.

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Traitement du signal et des images / Localisation et navigation

Article de conférence

RF Telecommunication Systems Characterization and Optimization

Auteur : Sombrin Jacques B.

In Proc. Indo-French Workshop on Microwave and Photonic Technologies (WS ITM), Madras, India, February 20-22, 2023.

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Communications numériques / Systèmes spatiaux de communication

Thèse de Doctorat

Signal Processing for GNSS Reflectometry

Auteur : Lubeigt Corentin

Defended on February 14, 2023.

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Global Navigation Satellite Systems (GNSS) Reflectometry, or GNSS-R, is the study of GNSS signals reflected from the Earth’s surface. These so-called signals of opportunity, usually seen as a nuisance in standard navigation applications, contain meaningful information on the nature and relative position of the reflecting surface. Depending on the receiver platform (e.g., ground-based, airplane, satellite) and the reflecting surface itself (e.g., rough sea, lake), the reflected signal, more or less distorted, is difficult to model, and the corresponding methods to estimate the signal parameters of interest may vary. This thesis starts from the navigation multipath problem in harsh environments, which can be seen as a dual source estimation problem where the main source is the signal of interest, and the secondary one is a single reflection of the main source. Depending on the scenario and the resources at hand, it is possible i) to estimate the parameters of interest (i.e., time-delay, Doppler frequency, amplitude and phase) of both sources, or ii) to estimate only one source’s parameters, although these estimates may be biased because of the interfering source. Either way, it is necessary to know the achievable performance for these estimation problems. For this purpose, tools from the estimation theory, such as the Cramér-Rao bound (CRB), can be used. In this thesis a CRB expression was derived for the properly specified case (dual source), and the misspecified one (single source). These bounds were compared to the performance obtained with different estimators, in order to theoretically characterize the problem at hand. This study allowed to establish a clear mathematical framework that also fits the groundbased GNSS-R problem, for which the reflected signal is little distorted by the reflecting surface. In this case, the direct and reflected signals are close in time, which inevitably leads to interference, or crosstalk, and then to a clear performance degradation. Standard GNSS-R techniques, which do not perform well in this ground-based scenario, were compared to the CRB and two proposed approaches: i) a Taylor approximation of the dual source likelihood criterion when both sources are very close in time, and ii) a dual source estimation strategy to reduce or cancel the crosstalk. This part on ground-based GNSS-R was supported by a real data set, obtained from a data collection campaign organized by CNES (Toulouse, France). The problem changes slowly when the satellite elevation increases : the reflection, assumed coherent so far, turns non-coherent because of the reflecting surface roughness. The automatic detection of this transition (i.e., from coherent to non-coherent) is of great interest for future satellite missions. Reflection coherence is mainly observed by looking at the relative phase between the reflected and direct signals. Consequently, a statistical study of phase difference time series allowed to build tests that depend on the time series Gaussianity or regularity. The proposed tests were applied to a data set provided by the IEEC (Barcelona, Spain). Finally, for scenarios where the reflecting surface distorts the signal significantly, it is necessary to adapt the signal model. The approach proposed in this thesis is to consider the received signal as a convolution between the transmitted signal and the reflecting surface impulse response. This signal model goes with the derivation of the corresponding CRB and the implementation of the maximum likelihood estimator. The question of the impulse response size determination, that is, the determination of the number of pulses required to describe the impulse response, was also tackled based on hypothesis tests. Simulation results show the potential of this approach.

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Traitement du signal et des images / Localisation et navigation

Présentation de soutenance de thèse

Signal Processing for GNSS Reflectometry

Auteur : Lubeigt Corentin

Defended on February 14, 2023.

Télécharger le document

Global Navigation Satellite Systems (GNSS) Reflectometry, or GNSS-R, is the study of GNSS signals reflected from the Earth’s surface. These so-called signals of opportunity, usually seen as a nuisance in standard navigation applications, contain meaningful information on the nature and relative position of the reflecting surface. Depending on the receiver platform (e.g., ground-based, airplane, satellite) and the reflecting surface itself (e.g., rough sea, lake), the reflected signal, more or less distorted, is difficult to model, and the corresponding methods to estimate the signal parameters of interest may vary. This thesis starts from the navigation multipath problem in harsh environments, which can be seen as a dual source estimation problem where the main source is the signal of interest, and the secondary one is a single reflection of the main source. Depending on the scenario and the resources at hand, it is possible i) to estimate the parameters of interest (i.e., time-delay, Doppler frequency, amplitude and phase) of both sources, or ii) to estimate only one source’s parameters, although these estimates may be biased because of the interfering source. Either way, it is necessary to know the achievable performance for these estimation problems. For this purpose, tools from the estimation theory, such as the Cramér-Rao bound (CRB), can be used. In this thesis a CRB expression was derived for the properly specified case (dual source), and the misspecified one (single source). These bounds were compared to the performance obtained with different estimators, in order to theoretically characterize the problem at hand. This study allowed to establish a clear mathematical framework that also fits the groundbased GNSS-R problem, for which the reflected signal is little distorted by the reflecting surface. In this case, the direct and reflected signals are close in time, which inevitably leads to interference, or crosstalk, and then to a clear performance degradation. Standard GNSS-R techniques, which do not perform well in this ground-based scenario, were compared to the CRB and two proposed approaches: i) a Taylor approximation of the dual source likelihood criterion when both sources are very close in time, and ii) a dual source estimation strategy to reduce or cancel the crosstalk. This part on ground-based GNSS-R was supported by a real data set, obtained from a data collection campaign organized by CNES (Toulouse, France). The problem changes slowly when the satellite elevation increases: the reflection, assumed coherent so far, turns non-coherent because of the reflecting surface roughness. The automatic detection of this transition (i.e., from coherent to non-coherent) is of great interest for future satellite missions. Reflection coherence is mainly observed by looking at the relative phase between the reflected and direct signals. Consequently, a statistical study of phase difference time series allowed to build tests that depend on the time series Gaussianity or regularity. The proposed tests were applied to a data set provided by the IEEC (Barcelona, Spain). Finally, for scenarios where the reflecting surface distorts the signal significantly, it is necessary to adapt the signal model. The approach proposed in this thesis is to consider the received signal as a convolution between the transmitted signal and the reflecting surface impulse response. This signal model goes with the derivation of the corresponding CRB and the implementation of the maximum likelihood estimator. The question of the impulse response size determination, that is, the determination of the number of pulses required to describe the impulse response, was also tackled based on hypothesis tests. Simulation results show the potential of this approach.

Lire la suite

Traitement du signal et des images / Localisation et navigation

Thèse de Doctorat

Precise Cooperative Positioning of Low-Cost Mobiles in an Urban Environment

Auteur : Verheyde Thomas

Defended on February 10, 2023.

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In recent years, our society has been preparing for a paradigm shift toward the hyperconnectivity of urban areas. This highly anticipated rise of connected smart city centers is led by the development of low-cost connected smartphone devices owned by each one of us. In this context, the demand for low-cost, high-precision localization solutions is driven by the development of novel autonomous systems. After Google announced the release of Android GNSS raw data measurements on mobile devices, the enthusiasm around those low-cost positioning devices quickly grew in the scientific community. The increasing need of Location Based Services (LBS) provoked the rapid evolution of smartphones embedded low-cost Global Navigation Satellite System (GNSS) chipsets within the last few years. Most Android devices are now equipped with multi-constellation and multi-frequency positioning units. Preliminary studies explored the implementation of advanced positioning algorithms aiming at answering the demand for precise navigation and positioning on mobile devices. However, various drawbacks prevent the realization of above-mentioned techniques on hand-held mobiles. Smartphones positioning capabilities are limited by the tight-integration of hardware components within the device. Integrated low-cost components, such as the linearly polarized antenna, are unoptimized for acquiring multi-frequency GNSS signals and their operation in constrained environment quickly becomes a challenge for mitigating disruptive multipath events. Moreover, due to a fierce technological competition between chipset manufacturers, embedded GNSS receivers have been conceived to act as ”blackbox” processes. The receiver parameterization is kept confidential and only GNSS raw data measurements are outputted to the user. In order to overcome those difficulties, this research work ambitions to develop a collaborative network positioning system between smartphones. A collaborative system is defined as a set of inter-connected users exchanging GNSS data in order to enhance network’s users positioning performance. The implementation of a cooperative smartphone network takes advantage of the tremendous number of connected Android devices present in today’s city centers for refining and improving users position accuracy and integrity in urban environment. This research thesis presents a thorough analysis of Android GNSS raw data measurements aiming at lifting the ambiguity generated by receivers’ ”black-box” processes on a wide variety of Android smartphone brand and models. A wide data collection campaign, on 7 different smartphone models in real-life urban conditions, has been conducted for assessing the positioning performance of those contemporary low-cost devices. After grasping the receivers’ mechanisms, the implementation of Android GNSS raw data measurements in collaborative positioning algorithm has been investigated. An innovative smartphone-based double code difference method has been employed to compute the inter-phone distance between network’s users, named Inter-Phone Ranging (IPR). This technique was tested for nominal and urban scenario cases and has demonstrated its reliability for collaborative positioning implementation. Finally, a smartphone-based cooperative engine, called SmartCoop, was developed and evaluated. This software-based engine is integrated within the cooperative network infrastructure for delivering accurate positioning solutions to network’s users. This collaborative estimation technique exploits the previously computed IPR ranges in a non-linear constrained optimization problem. An experimental protocol has been put in place in order to determine the estimation method efficiency through a series of simulation runs for both nominal and urban scenarios. The presented results analysis supports our hypothesis that smartphone-based collaborative engine enhances Android positioning performance in urban canyon.

Lire la suite

Communications numériques / Localisation et navigation

Présentation de soutenance de thèse

Precise Cooperative Positioning of Low-Cost Mobiles in an Urban Environment

Auteur : Verheyde Thomas

Defended on February 10, 2023.

Télécharger le document

In recent years, our society has been preparing for a paradigm shift toward the hyperconnectivity of urban areas. This highly anticipated rise of connected smart city centers is led by the development of low-cost connected smartphone devices owned by each one of us. In this context, the demand for low-cost, high-precision localization solutions is driven by the development of novel autonomous systems. After Google announced the release of Android GNSS raw data measurements on mobile devices, the enthusiasm around those low-cost positioning devices quickly grew in the scientific community. The increasing need of Location Based Services (LBS) provoked the rapid evolution of smartphones embedded low-cost Global Navigation Satellite System (GNSS) chipsets within the last few years. Most Android devices are now equipped with multi-constellation and multi-frequency positioning units. Preliminary studies explored the implementation of advanced positioning algorithms aiming at answering the demand for precise navigation and positioning on mobile devices. However, various drawbacks prevent the realization of above-mentioned techniques on hand-held mobiles. Smartphones positioning capabilities are limited by the tight-integration of hardware components within the device. Integrated low-cost components, such as the linearly polarized antenna, are unoptimized for acquiring multi-frequency GNSS signals and their operation in constrained environment quickly becomes a challenge for mitigating disruptive multipath events. Moreover, due to a fierce technological competition between chipset manufacturers, embedded GNSS receivers have been conceived to act as ”blackbox” processes. The receiver parameterization is kept confidential and only GNSS raw data measurements are outputted to the user. In order to overcome those difficulties, this research work ambitions to develop a collaborative network positioning system between smartphones. A collaborative system is defined as a set of inter-connected users exchanging GNSS data in order to enhance network’s users positioning performance. The implementation of a cooperative smartphone network takes advantage of the tremendous number of connected Android devices present in today’s city centers for refining and improving users position accuracy and integrity in urban environment. This research thesis presents a thorough analysis of Android GNSS raw data measurements aiming at lifting the ambiguity generated by receivers’ ”black-box” processes on a wide variety of Android smartphone brand and models. A wide data collection campaign, on 7 different smartphone models in real-life urban conditions, has been conducted for assessing the positioning performance of those contemporary low-cost devices. After grasping the receivers’ mechanisms, the implementation of Android GNSS raw data measurements in collaborative positioning algorithm has been investigated. An innovative smartphone-based double code difference method has been employed to compute the inter-phone distance between network’s users, named Inter-Phone Ranging (IPR). This technique was tested for nominal and urban scenario cases and has demonstrated its reliability for collaborative positioning implementation. Finally, a smartphone-based cooperative engine, called SmartCoop, was developed and evaluated. This software-based engine is integrated within the cooperative network infrastructure for delivering accurate positioning solutions to network’s users. This collaborative estimation technique exploits the previously computed IPR ranges in a non-linear constrained optimization problem. An experimental protocol has been put in place in order to determine the estimation method efficiency through a series of simulation runs for both nominal and urban scenarios. The presented results analysis supports our hypothesis that smartphone-based collaborative engine enhances Android positioning performance in urban canyon.

Lire la suite

Communications numériques / Localisation et navigation

Article de journal

Accounting for Acceleration – Signal Parameters Estimation Performance Limits in High Dynamics Applications

Auteurs : Mc Phee Hamish Scott, Ortega Espluga Lorenzo, Vilà-Valls Jordi et Chaumette Eric

IEEE Transactions on Aerospace and Electronic Systems, Vol 59, Issue 1, pp 610-622, February 2023.

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The derivation of estimation lower bounds is paramount to designing and assessing the performance of new estimators. A lot of effort has been devoted to the range-velocity estimation problem, a fundamental stage on several applications, but very few works deal with acceleration, being a key aspect in high dynamics applications. Considering a generic band-limited signal formulation, we derive a new general compact form Cramér-Rao bound (CRB) expression for joint time-delay, Doppler stretch, and acceleration estimation. This generalizes and expands upon known delay/Doppler estimation CRB results for both wideband and narrowband signals. This new formulation, especially easy to use, is created based on baseband signal samples, making it valid for a variety of remote sensors. The new CRB expressions are illustrated and validated with representative GPS L1 C/A and Linear Frequency Modulated (LFM) chirp band-limited signals. The mean square error (MSE) of a misspecified estimator (conventional delay/Doppler) is compared with the derived bound. The comparison indicates that for some acceleration ranges the misspecified estimator outperforms a well specified estimator that accounts for acceleration.

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Traitement du signal et des images / Localisation et navigation et Systèmes spatiaux de communication

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